{
  "id": "1607.08536",
  "version": "v1",
  "published": "2016-07-28T17:01:06.000Z",
  "updated": "2016-07-28T17:01:06.000Z",
  "title": "Existence results for fully nonlinear equations in radial domains",
  "authors": [
    "Giulio Galise",
    "Fabiana Leoni",
    "Filomena Pacella"
  ],
  "comment": "19 pages, 0 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the fully nonlinear problem \\begin{equation*} \\begin{cases} -F(x,D^2u)=|u|^{p-1}u & \\text{in $\\Omega$}\\\\ u=0 & \\text{on $\\partial\\Omega$} \\end{cases} \\end{equation*} where $F$ is uniformly elliptic, $p>1$ and $\\Omega$ is either an annulus or a ball in $\\Rn$, $n\\geq2$. \\\\ We prove the following results: \\begin{itemize} \\item[i)] existence of a positive/negative radial solution for every exponent $p>1$, if $\\Omega$ is an annulus; \\item[ii)] existence of infinitely many sign changing radial solutions for every $p>1$, characterized by the number of nodal regions, if $\\Omega$ is an annulus; \\item[iii)] existence of infinitely many sign changing radial solutions characterized by the number of nodal regions, if $F$ is one of the Pucci's operator, $\\Omega$ is a ball and $p$ is subcritical.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-28T17:01:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35B50",
      "34B15"
    ],
    "keywords": [
      "fully nonlinear equations",
      "existence results",
      "radial domains",
      "sign changing radial solutions",
      "nodal regions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}